Universal graphs with forbidden subgraphs and algebraic closure

We apply model theoretic methods to die problem of existence of countable u niversal graphs with finitely many forbidden connected subgraphs. We show t hat to a large extent the question reduces to one of local finiteness of an associated "algebraic closure" operator. The main applications art new exa mples of universal graphs with forbidden subgraphs and simplified treatment s of some previously known cases. (C) 1999 Academic Press.